Spatial profiles of a reaction-diffusion epidemic model with nonlinear incidence mechanism and varying total population

TL;DR

This paper analyzes a reaction-diffusion epidemic model with nonlinear transmission and varying population, examining how spatial profiles of infection change with different dispersal rates and population dynamics.

Contribution

It extends previous models by incorporating population variation and analyzes endemic equilibrium profiles under different dispersal scenarios.

Findings

Endemic equilibrium profiles depend on dispersal rates.

Varying population influences disease spread dynamics.

Numerical simulations support theoretical analysis.

Abstract

This paper considers a susceptible-infected-susceptible (SIS) epidemic reaction-diffusion model with no-flux boundary conditions and varying total population. The interaction of the susceptible and infected people is describe by the nonlinear transmission mechanism of the form $S^qI^p$, where $0<p\le 1$ and $q>0$. In [39], we have studied a model with a constant total population. In the current paper, we extend our analysis to a model with a varying total population, incorporating birth and death rates. We investigate the asymptotic profiles of the endemic equilibrium when the dispersal rates of susceptible and/or infected individuals are small. Our work is motivated by disease control strategies that limit population movement. To illustrate the main findings, we conduct numerical simulations and provide a discussion of the theoretical results from the view of disease control. We will also compare the results for the models with constant or varying total population.